On the Hierarchical Preconditioning of the Combined Field Integral Equation

This letter analyzes how hierarchical bases preconditioners constructed for the electric field integral equation can be effectively applied to the combined field integral equation (CFIE). For the case where no hierarchical solenoidal basis is available (e.g., on unstructured meshes), a new scheme is proposed: the CFIE is implicitly preconditioned on the solenoidal Helmholtz subspace by using a Helmholtz projector, while a hierarchical nonsolenoidal basis is used for the nonsolenoidal Helmholtz subspace. This results in a well-conditioned system. Numerical results corroborate the presented theory.